A controltheoretical look at Internet congestion control

1
A control-theoretical look at Internet
congestion control

• Fernando Paganini
• UCLA Electrical Engineering

• Collaborators
• J. Doyle, S. Low, S. Athuraliya, J. Wang
  (Caltech).
• Z. Wang, S. Adlakha (UCLA).

• Outline
• Current protocols and their dynamic behavior.
• A framework for analytical studies.
• A new design with scalable stability.

2
Controlling Internet Traffic

• Regulate transmission rates of end-to-end
  connections to use available bandwidth, but not
  exceed it (congestion).
• Possibly the largest-scale artificial feedback
  system
• When was the current system designed? Late 1980s.
• Who designed it? Internet, CS-type people, based
  on intuition, hacks,
• Where was the control community at the time?
  DGKF,
• Did they get it right? Yes and no.
• Yes the Internet works, survived explosive
  growth
• No performance is limited, future scalability in
  question.
• Can we do better? Yes, but we must work with
  tight information and implementation constraints.

3
Flow control problem

• L communication links shared by S sources.

Routing matrix
4
Current TCP Window Flow Control

• Lost packet detected by missing ACK ?
  retransmission.
• Transmission rate W packets per RTT.

5
Queue Management Policies at the Links

• DropTail drop packet when buffer overflows.
  Problem network operates with full queues,
  unnecessary delays.
• Active Queue Management warn of incipient
  congestion by probabilistically dropping packets
  before queue fills. e.g., Random Early Detection
  (RED, Floyd Jacobson 1993)

Combining Reno/RED, it was expected that the
network would operate around equilibrium with
small queues. However,
6
Dynamics of TCP/RED ns-2 simulations
50 identical FTP sources, single link 9 pkts/ms,
RED AQM
Window
Queue
Stable case, RTT 40ms
Unstable case, RTT 200ms
7
Fluid Modeling of TCP-Reno/RED
(Misra, Gong, Towsley, Hollot 00/01,
Low-Paganini-Doyle 01)
Additive Increase
Multiplicative Decrease

• Linearizing around equilibrium we find a
  stability region
• Unstable for high delay or, strikingly, high
  capacity!
• Packet simulations validate both the region and
  the oscillation
• frequency at the onset of instability.

8
A framework for new control laws
(Kelly et al, Low et al, Srikant et al.,)

• Idea express the feedback in terms of a scalar
  congestion measure
• or price p for each link. This could be loss
  probability, or also
• communicated to sources by an Explicit
  Congestion Notification bit.

p provides a barrier function or a Lagrange
multiplier for the constraint.

• Using this framework one can
• Characterize utility functions implicit in
  various protocols
• (what is maximized if they reach equilibrium)
  (Low 00).
• Study dynamic convergence to equilibrium. Main
  difficulty
• accounting for network delays.

9
Congestion control loop with delays
Routing/ Delay matrix
SOURCES
LINKS
10
Control objectives and design

• Track available capacity, yet almost empty
  queues.
• Stability in the presence of large variations in
  delay.
• Dynamic performance respond as quickly as
  possible.
• Difficulties for control synthesis
• Large-scale, coupled dynamics but decentralized
  control at links and sources, who only measure
  local information.
• Not just global variables, but the plant
  (routing, capacities, ) changes in a way unknown
  to sources/links. Must be robust.
• Delay can vary widely. However, sources can adapt
  to it.
• To top it off, solution must be simple
• Our approach
• Heuristic design aimed at the above objectives.
• Validated analytically by a stability proof.
• Performance verified empirically.

11
Design with delay compensation
12
Distributed gain compensation
SINGLE LINK
SOURCES
13
Nyquist argument for stability
Note if all delays are scaled by some constant,
the plot does not change.
In the time domain, only effect is a change in
time-scale of response.
14
Extension to arbitrary networks
Local analysis around equilibrium. Routing
matrices refer
here only to bottleneck links.
SOURCES
LINKS
p link prices
15
Local Stability result
16
From local to global design
17
Packet-level implementation
18
Packet-level simulation in ns-2
60 sources starting in groups of 20, RTT120ms. 1
link, 25 pkts/ms
Queue
Window
19
Conclusions

• Classical design heuristics MIMO analysis are
  able to provide a locally stable feedback
  control under widely varying operating
  conditions, and within very tight information
  constraints.
• From local to global extract nonlinear laws from
  linearization conditions at every point. This
  step leaves some degrees of freedom left for
  addressing equilibrium fairness, etc.
• Pending theory questions
• Global stability with both nonlinearity and
  delay.
• Equilibrium structure.
• Implementation issues
• Parameter settings some of them must be
  universal.
• The big one backward compatibility, incremental
  deployment did we arrive too late?